Theorems · Theorem · group theory
AddSubgroup.closure_closure_coe_preimage
∀ {G : Type u_1} [inst : AddGroup G] {k : Set G}, AddSubgroup.closure (Subtype.val ⁻¹' k) = ⊤- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Set.preimagestatement and proof · cited by 4,946
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- eq_top_iffproof · cited by 236
- AddMemClass.add_memproof · cited by 229
- ZeroMemClass.zero_memproof · cited by 162
- AddSubgroup.closurestatement and proof · cited by 156
- NegMemClass.neg_memproof · cited by 63
- AddSubgroup.subset_closureproof · cited by 49
- AddSubgroup.closure_inductionproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.closure_preimage_eq_topproof · cited by 1